Biological control mechanisms underlying entrainment to mechanical resonance

The neuronal circuit controlling the rhythmic movements in animal locomotion is called the central pattern generator (CPG). The biological control mechanism appears to exploit mechanical resonance to achieve efficient locomotion. The objective of this paper is to reveal the fundamental mechanism underlying entrainment of CPGs to resonance through sensory feedback. To uncover the essential principle, we choose to consider the simplest setting where a pendulum is driven by the reciprocal inhibition oscillator. Existence and properties of stable oscillations are examined by the harmonic balance method, which enables approximate but insightful analysis. The method predicts, and simulations confirm, that the resonance entrainment can be maintained robustly against parameter perturbations through two distinct mechanisms: negative rate feedback and positive integral feedback.